Experimental Investigation on the Proper Fatigue ... - CiteSeerX

Key Engineering Materials Vols. 297-300 (2005) pp. 2477-2482 online at http://www.scientific.net © 2005 Trans Tech Publications, Switzerland

Experimental Investigation on the Proper Fatigue Parameter of Cyclically Non-Stabilized Materials Seong Gu Honga, Keum Oh Leeb, Jae Yong Limc and Soon Bok Leed Department of Mechanical Engineering, Korea Advanced Institute of Science and Technology, Daejon, Republic of Korea a

[email protected], [email protected], [email protected], [email protected]

Keywords: Cyclical non-stabilization, Dynamic strain aging, Fatigue parameter, Plastic strain energy density, 316L stainless steel, 429EM stainless steel

Abstract. Low-cycle fatigue tests were carried out in air in a wide temperature range from room temperature to 650oC to investigate the role of temperature on the low-cycle fatigue behavior of two types of stainless steels, cold-worked (CW) 316L austenitic stainless steel and 429 EM ferritic stainless steel. CW 316L stainless steel underwent additional hardening at room temperature and in 250-600oC: plasticity-induced martensite transformation at room temperature and dynamic strain aging in 250-600oC. As for 429 EM stainless steel, it underwent remarkable hardening in 200-400oC due to dynamic strain aging, resulting in a continuous increase in cyclic peak stress until failure. Three fatigue parameters, such as stress amplitude, plastic strain amplitude and plastic strain energy density, were evaluated. The results revealed that plastic strain energy density is nearly invariant through a whole life and, thus, recommended as a proper fatigue parameter for cyclically non-stabilized materials. Introduction The currently widely used life prediction models such as the Coffin-Manson relation [1], S-N curves, and the energy-based models [2] are based on the assumption that the behavior of materials undergoing cyclic loading is stabilized (or saturated) during the initial stage, at least within several tens of cycles. However, in many materials, such a stabilized state is hardly achieved. Cyclic stress response of materials resultes from the competing mechanisms between hardening and softening. The activated mechanisms for cyclic hardening or softening depend on test conditions such as temperature, load amplitude and so on. Therefore, cyclic behavior of materials is very complicate and selecting a proper parameter, which may represent the state of materials during a whole life, will be important. In this study, two types of stainless steel, cold-worked 316L austenitic stainless steel and 429 EM ferritic stainless steel, were examined by performing low-cycle fatigue tests with varying temperature and strain amplitude. The activated mechanisms for cyclic hardening or softening at each temperature were investigated by analyzing the temperature dependece of cyclic stress response. Three fatigue parameters, such as stress amplitude, plastic strain amplitude and plastic strain energy density, were examined to determine which one is suitable for life prediction. Experiment The materials used in this study were cold-worked (CW) 316L austenitic stainless steel (SS) and 429EM ferritic SS having chemical compositions (wt. %): C-0.025 , Si-0.41, Mn-1.41, P-0.025, S-0.025, Ni-10.22, -16.16, Mo-2.09, and N-0.043 for 316L SS. C-0.021, Si-1.00, Mn-0.029, P-0.019, S-0.001, Ni-0.15, Cr-14.46, Mo-0.07, Al-0.08, Ti-0.15, Nb-0.34, Cu-0.45 and N-0.002 for 429EM SS. CW 316L SS was manufactured by the following process: material was solution-treated at 1100oC for 40 minutes, then water-quenched, and finally a round bar having a diameter of 16 mm was made through cold drawing which introduced a 17 % prestrain. 429EM SS was made through rolling from a plate with 80mm thickness to a plate with 20mm, and normalized at 850℃ for an hour. The Licensed to Korea Advanced Institute of Science and Technology KAIST - Daejeon - Korea South All rights reserved. No part of the contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of the publisher: Trans Tech Publications Ltd, Switzerland, www.ttp.net. (ID: 143.248.54.230-15/02/06,11:02:08)

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as-received materials were fabricated into the dog-bone type specimens having a gauge length of 36mm and a gauge diameter of 8mm in accordance with ASTM standard E606-92. A closed-loop servo-hydraulic test system with 5-ton capacity was used to perform LCF tests. A 3-zone resistance type furnace which controls temperature within a range of ±1oC at steady state was used for temperature control. A high temperature extensometer (MTS model no. : 632-13F-20) was used to control strain signal and measure strain. LCF tests were carried out in laboratory air and under fully-reversed total axial strain control mode using a triangular waveform. Test temperatures varies from room temperature (RT) to 650oC and applied strain amplitudes were from 0.3 to 0.8%. Strain rates were fixed as 1×10-3/s for CW 316L SS and 2×10-3/s for 429EM SS. Results and discussion

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CW 316L SS o 200 C Total strain amplitude 0.4 % 0.5 % 0.8 %

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Normalized peak stress

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Cyclic stress response. Cyclic stress response (CSR), which represents the evolution of tensile peak stress with the number of cycle, of two materials are depicted in Fig. 1 and Fig. 2 (the term, ‘normalized’ means that the value at each cycle is normalized with that at half-life). CSR of a material results from the interaction between the competing mechanisms of hardening and softening during deformation. CSR of two materials strongly depended on temperature. This implies that the activated mechanism for cyclic hardening or softening changed with temperature, causing the cyclically non-stabilized behavior of the materials.

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Fig. 1 Evolution of ∆σ/2 with life fraction in CW 316L SS: (a) RT, (b) 200oC and (c) 600oC 1) CW 316L stainless steel. Cyclic softening was predominant during a whole life at all test conditions because the as-received material was made through cold-drawing. It has been reported that cyclic softening dominates CSR of materials that are manufactured by the cold work process or have a high initial dislocation density. Cyclic softening of cold-worked materials occurs (1) when the annihilation rate of the dislocations is greater than their generation rate, causing a net decrease in the dislocation density, or (2) when the rearrangement of previously formed dislocation structure takes place, resulting in an increase in the mean free path of dislocations (dynamic recovery) [3]. That is, dynamic recovery dominates CSR of cold-worked materials during LCF deformation. However, as shown in Fig. 1 (a), the hardening in CSR was observed at RT above ∆εt/2=0.4%. It is well known that austenitic phase is metastable and, thus, martensitic transformation can be strongly promoted by plastic deformation applied in a range of temperature between Ms and Md, where Ms is the temperature for spontaneous transformation on cooling and Md is the maximum temperature at which the transformation can be induced under plastic deformation. Baudry and Pineau [4] reported that the cumulative plastic strain at initiation of the γ → α′ transformation is a function of ∆εt/2 and exponentially increases with a decrease in ∆εt/2. It indicates that, for plasticity-induced phase transformation, the applied strain amplitude should be larger than the critical value. In the present study, the critical strain amplitude required for martensitic transformation was about 0.4%. In the temperature region of 250-600oC, cyclic softening was significantly reduced, compared with other temperatures. This implies that additional hardening mechanisms are activated in this temperature

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region. Temperature-dependent processes, such as precipitation of second phase and dynamic strain aging, are considered as the responsible mechanisms. TEM studies on LCF failed specimens revealed M23C6 type carbide precipitates only beyond 600oC with low strain rates below 1×10-4/s. Therefore, in this study, precipitation hardening can be ruled out. Dynamic strain aging is the phenomenon of interaction between diffusing solute atoms and mobile dislocations during plastic deformation. It depends on deformation rate and temperature. Dynamic strain aging under LCF loading could be manifested in the forms of the plateau or the peak in the variation of cyclic peak stress with temperature, the negative temperature dependence of plastic strain amplitude or softening ratio, the negative SRS, and the negative strain rate dependence of plastic strain amplitude or softening ratio. DSA-induced hardening is thought to come from the following two mechanisms: (1) based on the impurity pinning model [5], DSA is a consequence of the pinning and regeneration of dislocations. The pinning of dislocations during deformation could result from the formation of either Snoek or Cottrell atmospheres. As the dislocations are immobilized by pinning, more dislocations have to be generated to maintain the imposed strain rate. The enhancement in dislocation density as a result of such a process has been revealed by TEM studies [6]. (2) According to the previous result [7], in the regime of DSA, the mechanism of interaction between mobile dislocations and solute atmospheres enhances the slip planarity and, thus, restricts the cross slip of screw dislocations. This mechanism reduces dynamic recovery and leads to the reduction of cyclic softening. 30

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Fig. 2 (a) Evolution of tensile peak stress and (b) anomalies associated with DSA in 429 EM SS 2) 429EM stainless steel. Fig. 2 (a) shows the temperature dependence of CSR at ∆εt/2=0.3%. Cyclic hardening was predominant during an initial stage at all test conditions. At room temperature and 600oC, CSR followed a general tendency of annealed materials: hardening at an early stage followed stabilization (saturation). In the temperature region of 200-400oC, however, a considerable initial hardening, compared with other temperatures, is noticed and the developed tensile peak stress continuously increases until the final failure. Similar results have been reported in AISI 420 [8], Fe-30%Cr alloy and Fe-20%Cr alloy [9]. It is attributed to DSA-induced hardening. The regime of DSA was evaluated using the anomalies associated with DSA. During tensile deformation, serrated yielding was observed in 300-500oC. Fig. 2 (b) shows the variation of work hardening rate (=dσ/dε) and strain rate sensitivity (= dσ / d ln ε& ) with temperature. Work hardening rate was calculated from the amount of stress increase in the strain range from 0.2 to 10% and strain rate sensitivity was calculated from the difference of flow stresses between two strain rates of 1.75×10-3/s and 5.25×10-2/s at a strain of 10%. The variation of work hardening rate with temperature shows the hump in 200-400oC at 1.75×10-3/s and in 300-500oC at 5.25×10-2/s. This anomaly is caused by DSA-induced hardening. The observed hump moves to higher temperature with an increase in strain rate indicating that the regime of DSA moves to higher temperature as strain rate increases. The negative SRS was observed in 200-400oC. Based on the results, it was found that DSA occurs in the temperature region

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of 200-400oC, causing a considerable initial hardening and a continuous increase in cyclic tensile peak stress until failure. (b)

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Fig. 3 Evolution of ∆εp/2 with life fraction in CW 316L SS: (a) RT, (b) 200oC and (c) 600oC

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Fig. 4 Evolution of ∆Wp with life fraction in CW 316L SS: (a) RT, (b) 200oC and (c) 600oC Normalized fatigue parameters

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Plastic strain energy density Peak stress Plastic strain amplitude

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Fig. 5 Evolution of fatigue parameters with the number of cycle in 429EM SS Fatigue parameters. As mentioned in the previous section, the activated mechanisms for cyclic hardening or softening changed with temperature, resulting in cyclical non-stabilization of materials. This indicates that stress amplitude is not suitable for a life prediction parameter since it significantly varies with the number of cycle during fatigue deformation. Thus, S-N curves can’t be applied in this case. Fig. 3 and Fig. 4 show the evolution of plastic strain amplitude, ∆εp/2, and plastic strain energy density, ∆Wp, in CW 316L SS with life fraction at each temperature (the value at each cycle is normalized by that at half-life). The variation of ∆εp/2 during fatigue deformation is considerable and can’t be neglected. That is, ∆εp/2 can’t be used as a fatigue parameter: the Coffin-Manson model [1] can’t be applied in this case. However, ∆Wp shows desirable features as a fatigue parameter. ∆Wp was stabilized at an early stage of life, compared with ∆σ/2 and ∆εp/2, and this stabilized state was maintained until N/Nf=0.8, where macrocracks initiate. Similar results were also observed in 429EM SS. Fig. 5 depicts the evolution of three fatigue parameters with the number of cycle at 400oC where DSA occurs. The variations of ∆σ/2 and ∆εp/2 with the number of cycle are considerable. On the

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contrary, ∆Wp is initially stabilized and nearly constant through a whole life. ∆Wp is a combination of stress and plastic strain which are inversely related and, thus, the variation of ∆Wp during fatigue deformation becomes relatively small, compared with ∆σ/2 and ∆εp/2. These results recommend ∆Wp as a proper fatigue parameter for cyclically non-stabilized materials because it is stabilized at an early stage of life and nearly constant through a whole life. Life prediction. According to Morrow [2], the plastic strain energy per cycle can be regarded as a composite measure of the amount of fatigue damage per cycle since cyclic plastic strain is related to the movement of dislocation, and cyclic stress is related to the resistance to their motion. The fatigue resistance of a metal can be characterized in terms of its capacity to absorb and dissipate plastic strain energy. This model uses ∆Wp as a life prediction parameter and is given as Eq. (1);

N mf ⋅ ∆W p = C

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Plastic strain energy density (MJ/m )

where m and C are material constants representing the fatigue exponent and the material energy absorption capacity, respectively. Curves of ∆Wp−Nf are presented in Fig. 6. The result shows that the Morrow model appears to provide a reasonable representation of the fatigue behavior under isothermal conditions for both of two materials. The materials constants used in Eq. (1) are given in Table 1. However, it is noted that material constants (m and C) vary with temperature. In the recent study [10], a new life prediction model using a plastic strain energy density has been developed to consider temperature effect on fatigue life and the results show a good agreement with the experimental results for both of two materials. CW 316L SS RT o 200 C o 400 C o 550 C o 600 C o 650 C Prediction

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Fig. 6 Life prediction using the Morrow model: (a) CW 316L SS and (b) 429EM SS Table 1 Materials constants in the Morrow model CW 316L SS 429EM SS

m C (MJ/m3) m C (MJ/m3)

RT 0.531 346 0.875 2399

200oC 0.558 278 0.802 1820

400oC 0.622 333 0.974 3631

550oC 0.639 268 -

600oC 0.666 281 0.954 2323

650oC 0.645 218 -

Conclusions Cyclic stress responses of two types of stainless steels strongly depended on temperature. CW 316L stainless steel underwent additional hardening at room temperature and in 250-600oC: hardening at room temperature came from plasticity-induced martensite transformation and hardening in 250-600oC was attributed to dynamic strain aging. These hardening mechanisms competed with softening mechanism induced by dynamic recovery, generally observed in cold worked materials,

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resulting in the cyclical non-stabilization of the material. As for 429 EM stainless steel, it shows general tendency of annealed materials at room temperature. In 200-400oC, however, it underwent severe hardening due to dynamic strain aging, resulting in a continuous increase in cyclic peak stress until failure. A plastic strain energy density was nearly invariant through a whole life for both of materials and, thus, recommended as a proper fatigue parameter. Life prediction based on a plastic strain energy density provided a reasonable representation of the fatigue behavior under isothermal condition. Acknowledgements This work was supported by Computer Aided Reliability Evaluation (CARE) National Research Laboratory in Korea Advanced Institute of Science and Technology (KAIST). References [1] L.F. Coffin Jr.: ASME Trans. Vol. 76 (1954), p. 931 [2] J.D. Morrow: ASTM STP 378 (1964), p. 45 [3] S. Ganesh Sundara Raman and K.A. Padmanabhan: Int. J. Fatigue Vol. 18 No. 2 (1996), p. 71 [4] G. Baudry and A. Pineau: Mater. Sci. Eng. A Vol. 28 (1977), p. 229 [5] Y. Bergsrom and W. Roberts: Acta Metall. Vol. 19 (1971), p. 1243 [6] V.S. Srinivasan, M. Valsan, R. Sandhya, K. Bhanu Sankara Rao, S.L. Mannan and D.H. Sastry: Int. J. Fatigue Vol. 21 (1999), p. 11 [7] S.G. Hong and S.B. Lee: J. Nucl. Mater. Vol. 328 No. 2-3 (2004), p. 232 [8] A.F. Armas, M. Avalos, I. Alvares-Armas, C. Petersen and R. Schmitt: J. Nucl. Mater. Vol. 258-263 (1998), p. 1204 [9] Y. Kaneko, Y. Nagai, H. Miyamoto, T. Mimaki and S. Hashimoto: Mater. Sci. Eng. A Vol. 319-321 (2001), p. 559 [10] K.O. Lee, S.G. Hong, S. Yoon and S.B. Lee: submitted to Int. J. Fatigue